Simplify the following expression: $\dfrac{6r^4}{22r^5}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{6r^4}{22r^5} = \dfrac{6}{22} \cdot \dfrac{r^4}{r^5} $ To simplify $\frac{6}{22}$ , find the greatest common factor (GCD) of $6$ and $22$ $6 = 2 \cdot 3$ $22 = 2 \cdot 11$ $ \mbox{GCD}(6, 22) = 2 $ $ \dfrac{6}{22} \cdot \dfrac{r^4}{r^5} = \dfrac{2 \cdot 3}{2 \cdot 11} \cdot \dfrac{r^4}{r^5} $ $\phantom{ \dfrac{6}{22} \cdot \dfrac{4}{5}} = \dfrac{3}{11} \cdot \dfrac{r^4}{r^5} $ $ \dfrac{r^4}{r^5} = \dfrac{r \cdot r \cdot r \cdot r}{r \cdot r \cdot r \cdot r \cdot r} = \dfrac{1}{r} $ $ \dfrac{3}{11} \cdot \dfrac{1}{r} = \dfrac{3}{11r} $